The NNLO non-singlet QCD analysis of parton distributions based on Bernstein polynomials

A non-singlet QCD analysis of the structure function $xF_3$ up to NNLO is performed based on the Bernstein polynomials approach. We use recently calculated NNLO anomalous dimension coefficients for the moments of the $xF_3$ structure function in $\nu N$ scattering. In the fitting procedure, Bernstein polynomial method is used to construct experimental moments from the $xF_3$ data of the CCFR collaboration in the region of $x$ which is inaccessible experimentally. We also consider Bernstein averages to obtain some unknown parameters which exist in the valence quark densities in a wide range of $x$ and $Q^2$. The results of valence quark distributions up to NNLO are in good agreement with the available theoretical models. In the analysis we determined the QCD-scale $\Lambda^ {\bar{MS}}_{QCD, N_{f}=4}=211$ MeV (LO), 259 MeV (NLO) and 230 MeV (NNLO), corresponding to $\alpha_s(M_Z^2)=0.1291$ LO, $\alpha_s(M_Z^2)=0.1150$ NLO and $\alpha_s(M_Z^2)=0.1142$ NNLO. We compare our results for the QCD scale and the $\alpha_s(M_Z^2)$ with those obtained from deep inelastic scattering processes.Comment: 20 pages, 7 figures, published in JHE

An Analytical Expression for the Non-Singlet Structure Functions at Small xx in the Double Logarithmic Approximation

A simple analytic expression for the non-singlet structure function $f_{NS}$ is given. The expression is derived from the result of Ref. [1] obtained by low $x$ resummation of the quark ladder diagrams in the double logarithmic approximation of perturbative QCD.Comment: 5 pages, A few comments and refs are adde

Asymptotic high energy behavior of the deeply virtual Compton scattering amplitude

We compute the deeply virtual Compton scattering (DVCS) amplitude for forward and backward scattering in the asymptotic limit. Since this calculation does not assume ordering of the transverse momenta, it includes important logarithmic contributions that are beyond those summed by the DGLAP evolution. These contributions lead to a power-like behavior for the forward DVCS amplitude.Comment: Latex, 22 pages, 5 Figures; references enhanced; typos correcte

On the Resummation of the αln⁡2zTermsforQEDCorrectionstoDeep−Inelastic\alpha \ln^2 z Terms for QED Corrections to Deep-Inelastic epScatteringand Scattering and e^+e^-$ Annihilation

The resummation of the $\alpha \ln^2(z)$ non-singlet contributions is performed for initial state QED corrections. As examples, the effect of the resummation on neutral-current deep-inelastic scattering and the $e^+ e^- \rightarrow \mu^+ \mu^-$ scattering cross section near the $Z^0$-peak is investigated.Comment: 11 pages Latex, including 3 eps-figure

FORM version 4.0

We present version 4.0 of the symbolic manipulation system FORM. The most important new features are manipulation of rational polynomials and the factorization of expressions. Many other new functions and commands are also added; some of them are very general, while others are designed for building specific high level packages, such as one for Groebner bases. New is also the checkpoint facility, that allows for periodic backups during long calculations. Lastly, FORM 4.0 has become available as open source under the GNU General Public License version 3.Comment: 26 pages. Uses axodra

Double deeply virtual Compton scattering off the nucleon

We study the double deeply virtual Compton scattering (DDVCS) process off the nucleon, through the scattering of a spacelike virtual photon with large virtuality resulting in the production of a timelike virtual photon, decaying into an e^+ e^- pair. This process is expressed in the Bjorken regime in terms of generalized parton distributions (GPDs) and it is shown that by varying the invariant mass of the lepton pair, one can directly extract the GPDs from the observables. We give predictions for the DDVCS cross section and beam helicity asymmetry and discuss its experimental feasibility.Comment: 4 pages, 4 figure

QCD threshold corrections to di-lepton and Higgs rapidity distributions beyond N2{}^2LO

We present threshold enhanced QCD corrections to rapidity distributions of di-leptons in the Drell-Yan process and of Higgs particles in both gluon fusion and bottom quark annihilation processes using Sudakov resummed cross sections. We have used renormalisation group invariance and the mass factorisation theorem that these hard scattering cross sections satisfy as well as Sudakov resummation of QCD amplitudes. We find that these higher order threshold QCD corrections stabilise the theoretical predictions under scale variations.Comment: 1+34 pages, four plot

Susy QCD and High Energy Cosmic Rays 1. Fragmentation functions of Susy QCD

The supersymmetric evolution of the fragmentation functions (or timelike evolution) within N=1 $QCD$ is discussed and predictions for the fragmentation functions of the theory (into final protons) are given. We use a backward running of the supersymmetric DGLAP equations, using a method developed in previous works. We start from the usual QCD parameterizations at low energy and run the DGLAP back, up to an intermediate scale -assumed to be supersymmetric- where we switch-on supersymmetry. From there on we assume the applicability of an N=1 supersymmetric evolution (ESAP). We elaborate on possible application of these results to High Energy Cosmic Rays near the GZK cutoff.Comment: 36 pages, 12 fig

Parton distribution functions from the precise NNLO QCD fit

We report the parton distribution functions (PDFs) determined from the NNLO QCD analysis of the world inclusive DIS data with account of the precise NNLO QCD corrections to the evolution equations kernel. The value of strong coupling constant \alpha_s^{NNLO}(M_Z)=0.1141(14), in fair agreement with one obtained using the earlier approximate NNLO kernel by van Neerven-Vogt. The intermediate bosons rates calculated in the NNLO using obtained PDFs are in agreement to the latest Run II results.Comment: 8 pages, LATEX, 2 figures (EPS